Top-quark pair production close to threshold: Top-quark mass, width, and momentum distribution

The complete next-to-next-to-leading order (NNLO) QCD corrections to the total cross section sigma(e(+)e(-) --> Z*, gamma* --> t (t) over bar), in the kinematic region close to the top-quark-top-antiquark threshold, are calculated by solving the corresponding Schrodinger equations exactly in momentum space in a consistent momentum cutoff regularization scheme. The corrections coming from the same NNLO QCD effects to the top-quark three-momentum distribution d sigma/d\(k) over right arrow(t)\ are determined. We discuss the origin of the large NNLO corrections to the peak position and the normalization of the total cross section observed in previous works and propose a new top-quark mass definition, the IS mass Mis, which stabilizes the peak in the total cross section. If the influence of beamstrahlung and initial state radiation on the mass determination is small, a theoretical uncertainty on the 1S top-quark mass measurement of 200 MeV from the total cross section at the linear collider seems possible. We discuss how well the 1S mass can be related to the <(MS)over bar> mass. We propose a consistent way to implement the top-quark width at NNLO by including electroweak effects into the NRQCD matching coefficients, which can then become complex. [S0556-2821(99)07219-7].